Partial Decode-and-Forward Rates for the Gaussian MIMO Relay Channel: Inner Approximation of Non-Convex Rate Constraints

In this paper, we consider achievable partial decode-and-forward (PDF) rates for the Gaussian multiple-input multiple-output ( MIMO) relay channel. The PDF scheme generalizes the decode-and-forward (DF) scheme as it allows to optimize the amount of information that is transmitted in cooperation with the relay. For the Gaussian channel case, the optimal channel inputs for the PDF scheme are unknown, and even if Gaussian channel inputs are used, the resulting optimization problem (OP) is non-convex. Thus, suboptimal approaches are necessary in order to efficiently evaluate PDF rates. In this paper, we apply the so-called Inner Approximation Algorithm (IAA). By successively refining an approximation of the original OP, we are able to evaluate PDF rates by solving a sequence of convex OPs. Our simulation results show that these suboptimal PDF rates are able to outperform the rates achieved by point-to-point (P2P) transmission and the DF scheme. For scenarios where the source is equipped with more antennas than the relay, the suboptimal PDF rates even approach the cut-set bound (CSB).